In a context of ever-growing interest in stereoscopic systems, but where no standardized algorithmic methods of stereoscopic quality assessment exist, our work stands as a step forward in the understanding of the human perception and judgment mechanisms related to the multidimensional concept of stereoscopic image quality. We used a series of tools in order to perform in-depth investigations in this direction: we proposed an adapted framework to structure the process of stereoscopic quality assessment, we implemented a stereoscopic system in our laboratory for performing various tests, we created three stereoscopic datasets with precise structures, and we performed several experimental studies using these datasets. The numerous experimental data obtained were used in order to propose a first mathematical framework for explaining the overall percept of stereoscopic quality in function of the physical parameters of the stereoscopic images under study.